Constraints on stable equilibria with fluctuation-induced forces

Sahand Jamal Rahi 1, Mehran Kardar 1, Thorsten Emig 2, 3

Physical Review Letters 105 (2010) 070404

We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges, and show that any arrangement in space is unstable to small perturbations in position. This extends Earnshaw's theorem for electrostatics by including thermal fluctuations of internal charges. Quantum fluctuations of the electromagnetic field are responsible for Casimir/van der Waals interactions. Neglecting permeabilities, we find that any equilibrium position of items subject to such forces is also unstable if the permittivities of all objects are higher or lower than that of the enveloping medium; the former being the generic case for ordinary materials in vacuum.

  • 1. Department of Physics,
    Massachusetts Institute of Technology
  • 2. Institut für Theoretische Physik,
    Universität zu Köln
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud